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home about accordion guy google+ twitter subscribe - joey devilla's mobile/tech blog i will teach you data science, part 2: similar people and manhattan distance by joey devilla on august 13, 2018 this is the second in a series of articles where i’ll get you started on the basics of data science with python. in this article, we’ll take our first step in building recommendation systems: determining how similar people are by measuring the manhattan distance between them. you’ll want the following before you proceed any further: the previous article. it’s a good introduction to the series. the book: a programmer’s guide to data mining: the ancient art of the numerati — it’s free to download, and it’s the book we’ll use for the next little while. python 3: yes, you may have python 2 on your system right now, but it’s 2018. get python 3 — preferably python 3.6 or later. chapter 2 of a programmer’s guide to data mining: the ancient art of the numerati is about building recommendation systems. many recommendation systems are based on the idea that people similar to you often like similar things. their trick is to find people who like things that you like, and show you things that you might not have seen yet. for example, here’s a screenshot from my amazon account, which shows kindle magazines they’ll think i’ll like, based on my browsing, purchasing, rating history, and who-knows-what-else: the chapter’s exercises in building a simple recommendation engine make use of the information in the table shown below, which shows 8 people’s ratings of 8 bands that you’d likely hear on an alt-rock station circa 2012: click the table to see it at full size. each person has rated a number of the 8 bands on a scale of 1 (“hate them”) to 5 (“love them”). no one in the group has rated all 8 bands. your first question — and the question we’ll try to answer in this article — should be “how do i tell how similar any two people in this table are?”. i’ll start with some theory, but you’ll see actual code by the end of the article. similarity and distance before explaining how to figure out how similar any two people in the 8-by-8 table of people and bands are, zacharski (the author of a programmer’s guide to data mining: the ancient art of the numerati ) starts with a simpler data set: three people, who’ve rated two books on a scale of 0 (worst) to 5 (best): the cyber-thrllers snow crash and the girl with the dragon tattoo… book amy’s rating bill’s rating jim’s rating the girl with the dragon tattoo 5 5 4 snow crash 5 2 1 if you were to plot each person’s rating for the books as a single point on a two-dimensional graph, with the girl with the dragon tattoo as the x-axis and snow crash as the y-axis, you’d get this: image from a programmer’s guide to data mining: the ancient art of the numerati . the graph makes it easy to see whose tastes are similar. the closer any two people’s points are, the more similar their tastes in cyber-thriller books are. simply by looking at the graph, you can see that jim’s taste is more similar to bill’s than it is to amy’s, bill’s is more similar to amy’s than jim’s is, and bill’s is more similar to jim’s than his is to amy’s. while it’s easy for us humans to visually tell whose tastes are similar, it’s much easier to have a program do it mathematically, and there are a number of ways to do it. let’s look at the simplest way: calculating the manhattan distance between any two points. manhattan distance there’s a joke about the difference between the directions given to you by google maps and waze: google maps will suggest an alternate road to cut down your travel time; waze will suggest a shortcut through someone’s living room. the manhattan distance between two points is more like the google maps suggestion. it’s the simplest, computationally least expensive way to compute the distance between two points on a grid. it gets the name “manhattan” from the way you’d have to travel from one point to another by cab in manhattan’s grid of streets: only horizontally or vertically, with no diagonals allowed: the manhattan distance between a point located at (x1, y1) and another point at (x2, y2) is simply: x-distance between the points + y-distance between the points or, more mathematically: | x1 – x2 | + | y1 – y2 | looking at the dragon tattoo/snow crash graph… …we can calculate the manhattan distance between bill and jim: | 5 – 4 | + | 2 – 1 | = 2 and the manhattan distance between jim and amy: | 4 – 5 | + | 1 – 5 | = 5 using manhattan distance with more than two dimensions in the previous example, we were dealing with a two-dimensional space, where ratings for the girl with the dragon tattoo form one dimension, and ratings for snow crash form another. let’s go back to the “people and bands” study and look at two of the people, jordyn and sam. here’s a smaller table that shows only their ratings, and the differences between their ratings for each band: band jordyn’s rating for that band sam rating for that band difference between jordyn’s rating and sam’s rating blues traveler – 5 n/a broken bells 4.5 2 2.5 deadmau5 4 – n/a norah jones 5 3 2 phoenix 5 5 0 slightly stoopid 4.5 4 0.5 the strokes 4 5 1 vampire weekend 4 – n/a note that jordyn and sam didn’t rate all the bands. to calculate the manhattan distance between them, we need to work with only those bands that they both rated. here’s what the table looks like with only those bands: band jordyn’s rating for that band sam rating for that band difference between jordyn’s rating and sam’s rating broken bells 4.5 2 2.5 norah jones 5 3 2 phoenix 5 5 0 slightly stoopid 4.5 4 0.5 the strokes 4 5 1 now we can calculate the manhattan distance between jordyn’s and sam’s musical tastes. it’s not all that different from the first manhattan distance we calculated — it’s simply the sum of all the differences between their ratings for each band, or: difference between jordyn’s and sam’s ratings for broken bells + difference between jordyn’s and sam’s ratings for norah jones + difference between jordyn’s and sam’s ratings for phoenix + difference between jordyn’s and sam’s ratings for slightly stoopid + difference between jordyn’s and sam’s ratings for the strokes which is: | 4.5 – 2 | + | 5 – 3 | + | 5 – 5 | + | 4.5 – 4 | + | 4 – 5 | = 6. given that jordyn and sam are rating 5 bands on a scale of 1 to 5 (where 1 is “hate them” and 5 is “love them”), their manhattan distance can range from… 0, which means that they love these 5 bands equally, to 20, which means that they have completely opposite opinions of each of the 5 bands. with a manhattan distance of 6 (out of maximum of 20) based on 5 bands that are pretty likely to appear on a single spotify playlist, it would be fair to say that musically speaking, jordyn and sam are more alike than dissimilar. calculating manhattan distance, the book’s way if you remember the previous article in this series or are following along with the book, you know that the “people and bands” data is expressed in code using a python dictionary, as shown below: python users = { "angelica": { "blues traveler": 3.5, "broken bells": 2.0, "norah jones": 4.5, "phoenix": 5.0, "slightly stoopid": 1.5, "the strokes": 2.5, "vampire weekend": 2.0 }, "bill": { "blues traveler": 2.0, "broken bells": 3.5, "deadmau5": 4.0, "phoenix": 2.0, "slightly stoopid": 3.5, "vampire weekend": 3.0 }, "chan": { "blues traveler": 5.0, "broken bells": 1.0, "deadmau5": 1.0, "norah jones": 3.0, "phoenix": 5, "slightly stoopid": 1.0 }, "dan": { "blues traveler": 3.0, "broken bells": 4.0, "deadmau5": 4.5, "phoenix": 3.0, "slightly stoopid": 4.5, "the strokes": 4.0, "vampire weekend": 2.0 }, "hailey": { "broken bells": 4.0, "deadmau5": 1.0, "norah jones": 4.0, "the strokes": 4.0, "vampire weekend": 1.0 }, "jordyn": { "broken bells": 4.5, "deadmau5": 4.0, "norah jones": 5.0, "phoenix": 5.0, "slightly stoopid": 4.5, "the strokes": 4.0, "vampire weekend": 4.0 }, "sam": { "blues traveler": 5.0, "broken bells": 2.0, "

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Domain Name: GLOBALNERDY.COM
Registry Domain ID: 555885889_DOMAIN_COM-VRSN
Registrar WHOIS Server: whois.tucows.com
Registrar URL: http://www.tucows.com
Updated Date: 2015-08-07T23:24:28Z
Creation Date: 2006-08-16T02:43:52Z
Registry Expiry Date: 2021-08-16T02:43:52Z
Registrar: Tucows Domains Inc.
Registrar IANA ID: 69
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Domain Status: clientTransferProhibited https://icann.org/epp#clientTransferProhibited
Domain Status: clientUpdateProhibited https://icann.org/epp#clientUpdateProhibited
Name Server: NS1.PRESSHARBOR.COM
Name Server: NS2.PRESSHARBOR.COM
DNSSEC: unsigned
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  REGISTRAR Tucows Domains Inc.

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  ARGS domain =globalnerdy.com

  PORT 43

  TYPE domain

DOMAIN

  NAME globalnerdy.com

  CHANGED 2015-08-07

  CREATED 2006-08-16

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  NS1.PRESSHARBOR.COM 23.111.131.102

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